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EMR 6500: Survey Research

EMR 6500: Survey Research. Dr. Chris L. S. Coryn Kristin A. Hobson Spring 2013. Agenda. Systematic sampling Cluster sampling for means and totals. Systematic Sampling. Systematic Sampling.

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EMR 6500: Survey Research

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  1. EMR 6500:Survey Research Dr. Chris L. S. Coryn Kristin A. Hobson Spring 2013

  2. Agenda Systematic sampling Cluster sampling for means and totals

  3. Systematic Sampling

  4. Systematic Sampling Systematic sampling simplifies the sample selection process compared to both simple random sampling and stratified random sampling In systematic sampling an interval (k) is used to select sample elements The starting point is (should be) selected randomly

  5. Systematic Sampling • Systematic sampling is a useful alternative to simple random sampling because: • It is easier to perform in the field and less subject to selection errors, especially if a good frame is not available • It can provide greater information per unit cost than simple random samples for populations with certain patterns in the arrangement of elements

  6. 1-in-k Systematic Sampling • Divide the population size N by the desired sample size n • Let k = N/n • k must be equal to or less than N/n (i.e., k ≤ N/n) • If N = 15,000 and n = 100, then k≤ 150

  7. 1-in-k Systematic Sampling • If N were 1,000 and nwere 100 • k would equal 1,000/100 = 10 • If k = 10, the start value would range between 1 to 10 and all selections thereafter would be every 10th entry on the sampling frame • If the start value was 8, then the next selection would be 18, followed by 28, and so forth

  8. Random Population Elements

  9. Ordered Population Elements

  10. Periodic Population Elements

  11. Estimation of a Population Mean and Total

  12. Estimation of a Population Mean *Note: This formula assumes a randomly ordered population

  13. Estimation of a Population Total *Note: This formula assumes a randomly ordered population

  14. Estimation of a Population Proportion

  15. Estimation of a Population Proportion *Note: This formula assumes a randomly ordered population

  16. Selecting the Sample Size

  17. Sample Size for Estimating a Population Mean

  18. Sample Size for Estimating a Population Proportion

  19. Variance Estimation for Ordered and Periodic Distributions

  20. Variance Estimates • Repeated systematic sampling • Divides a systematic sample into smaller systematic samples to approximate a random population • Multiple 1-in-k systematic samples • Successive difference method • A samples of size n yields n-1 successive differences that are used to estimate variance • Best choice when population elements are not randomly ordered

  21. Cluster Sampling

  22. Cluster Sampling Cluster sampling is a probability sampling method in which each sampling unit is a collection, or cluster, of elements Clusters can consist of almost any imaginable natural (and artificial) grouping of elements

  23. Cluster Sampling • Cluster sampling is an effective sampling design if: • A good sampling frame listing population elements is not available or is very costly to obtain, but a frame listing clusters is easily obtained • The cost of obtaining observations increases as the distance separating elements increases

  24. Cluster Sampling Unlike stratified random sampling, in which strata are ideally similar within stratum and where stratum should differ from one another, clusters should be different within clusters and be similar between clusters

  25. Cluster Sampling Notation

  26. Estimation of a Population Mean and Total

  27. Estimation of a Population Mean *Note: takes the form of a ratio estimator, with taking the place of *Note: can be estimated by if M is unknown

  28. Example for a Population Mean

  29. Example for a Population Mean

  30. Example for a Population Mean *Note: Because M is not known, is estimated by

  31. Example for a Population Mean

  32. Estimation of a Population Total

  33. Estimation of a Population Total

  34. Estimation of a Population Total that Does not Depend on M

  35. Example of Estimation of a Population Total that Does not Depend on M

  36. Example of Estimation of a Population Total that Does not Depend on M

  37. Equal Cluster Sizes

  38. Equal Cluster Sizes for Estimating a Population Mean All mi values are equal to a common, or constant, value m In this case, M = Nm, and the total sample size is nm elements (n clusters of m elements each) When cluster sizes are equal m1 = m2 = mN Variance components analysis simplifies estimating the variance using ANOVA methods

  39. Equal Cluster Sizes for Estimating a Population Mean

  40. ANOVA Method • There are 4,000 households (elements) • There are 400 geographical regions (clusters) • There are 10 households in each region

  41. ANOVA Method

  42. ANOVA Method *Note: ‘Factor’ denotes between-cluster variation and ‘Error’ denotes within cluster variation

  43. ANOVA Method

  44. Selecting the Sample Size for Estimating Population Means and Totals

  45. Sample Size for Estimating Population Means Where is estimated by

  46. Example of Sample Size for Estimating Population Means How large a sample should be taken to estimate the average per-capita income with a bound on the error of estimation of B = $500?

  47. Example of Sample Size for Estimating Population Means *Note: Because M is not known, is estimated by

  48. Example of Sample Size for Estimating Population Means

  49. Sample Size for Estimating Population Totals When M is Known Where is estimated by

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